{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Convolutional auto-encoder"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Extracting data/train-images-idx3-ubyte.gz\n",
      "Extracting data/train-labels-idx1-ubyte.gz\n",
      "Extracting data/t10k-images-idx3-ubyte.gz\n",
      "Extracting data/t10k-labels-idx1-ubyte.gz\n",
      "Packages loaded\n"
     ]
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import math\n",
    "import tensorflow as tf\n",
    "import tensorflow.examples.tutorials.mnist.input_data as input_data\n",
    "%matplotlib inline \n",
    "\n",
    "mnist = input_data.read_data_sets(\"data/\", one_hot=True)\n",
    "trainimgs   = mnist.train.images\n",
    "trainlabels = mnist.train.labels\n",
    "testimgs    = mnist.test.images\n",
    "testlabels  = mnist.test.labels\n",
    "ntrain      = trainimgs.shape[0]\n",
    "ntest       = testimgs.shape[0]\n",
    "dim         = trainimgs.shape[1]\n",
    "nout        = trainlabels.shape[1]\n",
    "print (\"Packages loaded\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# DEFINE NETWORKS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Network ready\n"
     ]
    }
   ],
   "source": [
    "n1 = 16\n",
    "n2 = 32\n",
    "n3 = 64\n",
    "ksize = 5\n",
    "weights = {\n",
    "    'ce1': tf.Variable(tf.random_normal([ksize, ksize, 1, n1],  stddev=0.1)),\n",
    "    'ce2': tf.Variable(tf.random_normal([ksize, ksize, n1, n2], stddev=0.1)),\n",
    "    'ce3': tf.Variable(tf.random_normal([ksize, ksize, n2, n3], stddev=0.1)),\n",
    "    'cd3': tf.Variable(tf.random_normal([ksize, ksize, n2, n3], stddev=0.1)),\n",
    "    'cd2': tf.Variable(tf.random_normal([ksize, ksize, n1, n2], stddev=0.1)),\n",
    "    'cd1': tf.Variable(tf.random_normal([ksize, ksize, 1, n1],  stddev=0.1))\n",
    "}\n",
    "biases = {\n",
    "    'be1': tf.Variable(tf.random_normal([n1], stddev=0.1)),\n",
    "    'be2': tf.Variable(tf.random_normal([n2], stddev=0.1)),\n",
    "    'be3': tf.Variable(tf.random_normal([n3], stddev=0.1)),\n",
    "    'bd3': tf.Variable(tf.random_normal([n2], stddev=0.1)),\n",
    "    'bd2': tf.Variable(tf.random_normal([n1], stddev=0.1)),\n",
    "    'bd1': tf.Variable(tf.random_normal([1],  stddev=0.1))\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def cae(_X, _W, _b, _keepprob):\n",
    "    _input_r = tf.reshape(_X, shape=[-1, 28, 28, 1])\n",
    "    # Encoder\n",
    "    _ce1 = tf.nn.sigmoid(tf.add(tf.nn.conv2d(_input_r, _W['ce1']\n",
    "        , strides=[1, 2, 2, 1], padding='SAME'), _b['be1']))\n",
    "    _ce1 = tf.nn.dropout(_ce1, _keepprob)\n",
    "    _ce2 = tf.nn.sigmoid(tf.add(tf.nn.conv2d(_ce1, _W['ce2']\n",
    "        , strides=[1, 2, 2, 1], padding='SAME'), _b['be2'])) \n",
    "    _ce2 = tf.nn.dropout(_ce2, _keepprob)\n",
    "    _ce3 = tf.nn.sigmoid(tf.add(tf.nn.conv2d(_ce2, _W['ce3']\n",
    "        , strides=[1, 2, 2, 1], padding='SAME'), _b['be3'])) \n",
    "    _ce1 = tf.nn.dropout(_ce3, _keepprob)\n",
    "    # Decoder\n",
    "    _cd3 = tf.nn.sigmoid(tf.add(tf.nn.conv2d_transpose(_ce3, _W['cd3']\n",
    "        , tf.pack([tf.shape(_X)[0], 7, 7, n2]), strides=[1, 2, 2, 1]\n",
    "        , padding='SAME'), _b['bd3'])) \n",
    "    _cd3 = tf.nn.dropout(_cd3, _keepprob)\n",
    "    _cd2 = tf.nn.sigmoid(tf.add(tf.nn.conv2d_transpose(_cd3, _W['cd2']\n",
    "        , tf.pack([tf.shape(_X)[0], 14, 14, n1]), strides=[1, 2, 2, 1]\n",
    "        , padding='SAME') , _b['bd2'])) \n",
    "    _cd2 = tf.nn.dropout(_cd2, _keepprob)\n",
    "    _cd1 = tf.nn.sigmoid(tf.add(tf.nn.conv2d_transpose(_cd2, _W['cd1']\n",
    "        , tf.pack([tf.shape(_X)[0], 28, 28, 1]), strides=[1, 2, 2, 1]\n",
    "        , padding='SAME'), _b['bd1'])) \n",
    "    _cd1 = tf.nn.dropout(_cd1, _keepprob)\n",
    "    _out = _cd1\n",
    "    return {'input_r': _input_r, 'ce1': _ce1, 'ce2': _ce2, 'ce3': _ce3\n",
    "        , 'cd3': _cd3, 'cd2': _cd2, 'cd1': _cd1\n",
    "        , 'layers': (_input_r, _ce1, _ce2, _ce3, _cd3, _cd2, _cd1)\n",
    "        , 'out': _out}\n",
    "print (\"Network ready\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# DEFINE FUNCTIONS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Functions ready\n"
     ]
    }
   ],
   "source": [
    "x = tf.placeholder(tf.float32, [None, dim])\n",
    "y = tf.placeholder(tf.float32, [None, dim])\n",
    "keepprob = tf.placeholder(tf.float32)\n",
    "pred = cae(x, weights, biases, keepprob)['out']\n",
    "cost = tf.reduce_sum(tf.square(cae(x, weights, biases, keepprob)['out'] \n",
    "            - tf.reshape(y, shape=[-1, 28, 28, 1])))\n",
    "learning_rate = 0.001\n",
    "optm = tf.train.AdamOptimizer(learning_rate).minimize(cost)\n",
    "init = tf.initialize_all_variables()\n",
    "print (\"Functions ready\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# OPTIMIZE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Strart training..\n",
      "[00/05] cost: 8200.5146\n"
     ]
    },
    {
     "data": {
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TTguP4514gZg2V3dd5xRwQFyiVquELhfzMnWxXbOBaE16+umnQ5umU1XbDu8i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\nlXrLre+zud1JZu0aWzKb2SkVbKzdzcw+evQo2faZtWWYpXgO8spsbJy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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f71795f4c10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[01/05] cost: 3641.4082\n"
     ]
    },
    {
     "data": {
      "image/png": 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BMFr+diyA/Nr9RQDuRReC6Nu3byqz/UCX7HSZi3cf5VS3AHDEEUeEOi9zadpF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\nEEIIIYQQQgghxo3/AZSunKq61Br6AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f711c393b90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[02/05] cost: 2731.7280\n"
     ]
    },
    {
     "data": {
      "image/png": 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7autyn+6kyvYNtkYAuTsf626pnO5R7T+6fPmVr3wlKWtKUl3uu/7665Oy7jyu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\nsONv81I2zVbb9a5a0+uL91TS8Vvn1RqvVm373BTy2Zcac9M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lb9y40dmrVq1SsSNHjihf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\nCCHEN/4HHiVouFRID2sAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f71140f81d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[03/05] cost: 2320.9961\n"
     ]
    },
    {
     "data": {
      "image/png": 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pDXVjygVr1lQa1qypNKxZU2lYszVCIba06QDq5G9nA8jmXLwZwGNoRBC8grSu\nNsroaqO8Oqpaa9QCxtOxmoJUU/fylN5//ud/hjZNKclTbZqOV6f/ND3fwoULU1ntYppWetGiRams\nK25z+mAgpjfV9Hv/9E//FOqcKk/TwdYARWsWiLYIPidqldL025y6W+2IrHGdAv7CF74Q6suXL0/l\nCy64ILTxSvRA1MjmzZtDm6Z35GtFUzJq2vFx48alstp2eLpYU6iznoF4/NTKpPvLKz7r8asBWqVZ\ntufcf//9qazHkVcyB2KKW7U8sg1A7WL/+7//G+pspdR+WK04bBfSFOSaqpq1d84554S2P/3pT6G+\nzz77pPIvf/nL0MbXnPbJavHl+8QNN9wQ2m6++eZQv+yyy1J5zpw5qawpUKuUVmmW7S18X1cN6NiB\n+zy9x//9739PZbUR66rrbDfXVdbVEs46VAsvp3PWfTjttNNCmy5BwZYktffwfeCYY44JbTpe4etc\nrZ5qwb/rrrtSWfvvGqBVmmWrF4cy8LkCYh+s79N7r1q5+fxoSnK1bvE+qH40zIHvv9pH631Crzke\n6+g4VdPjs21TLaZq158yZUoq63hA9/G2225L5bPPPhvNUWxCgX7ITO2h4f9+eV5rTDlgzZpKw5o1\nlYY1ayoNa7YKKUW2tPqGf8ZUCtasqTSsWVNpWLOm0rBmq4Ris6WtAdAfwGoAAwA0mrqAp+a3bNkS\nMoOY9mHp0qXBLlHDFKRZIGYoqa+vD9llTNuzePFizJo1q6N3oxwoWLOc/eatt97KyUxn2pZXX301\nx5pSoxSsWc7ct2nTppwMYKZtefPNN63ZDAVrli1Y++23X06WXdP2bNiwISfrZ2MU+3BzH4DLAPx7\nw//3NPaik08+OZVvu+225ENUf6v6+zgNnbaxrxoAnnnmmVTmNJBAblwNxyCceuqpoY1TSgPRY/jg\ngw+GNk1vp/EvHO+i+6u+9m984xuprD5tje1hfzEfWyCmbWX69++f4z2uUQrSLBA9sJ07d07puzkN\nJJCbZveRRx5JZfVEf+UrX0llTWOo5501c8IJJ4Q29U9z2lpNG8mpH4Go8Z122im0qReW/bu870C8\njvTBT48Rx3RovJl6hPm65zS/fI3XGAVrlv3J3Mcccsgh4XUa78XpzDV9MvcpGpOlfu4DDzwwlTk2\nEMiNdbj77rtTWeMD1q1bF+ocr6Mpbjn1OhD1rbpkHWqM23XXXRfqHDemA25OkQ7siB/ab7/9QgpX\nTnFaYxT6FMCqAAAgAElEQVSsWU4Ly/FUOuDWvoljHzWOjwebkyZNCm0aN8ZxhRp7ouMBjjPQ/lvj\nDHl8oDEHeh3tu+++qaya5VT5GuOmPxTz/vP4A8j93j179kz/848g+j1qiII1y/FVM2bMwIwZMwAA\nn/rUp8LrdImEb33rW6ms98gXX3wx1DmOT+OuL7roolDPnksgt6/ScemECRNSWTWhse2aRprjEDUV\n+htvvBHq3N9z/DmQ+915HKJjZY2v53hRvcc0RiG2tNsBPAVgBIAVAC4H8CMAH0Emdd6JDXVjygVr\n1lQa1qypNKxZU2lYszVCITM3FzXx95Ob+LsxHY01ayoNa9ZUGtasqTSs2RqhFAkFjDHGGGOMMabD\nKTbmpiB4PYGzzjorldV7r7489uKuWbMmtKmPcNCgQal8wAEHhDb1EbJPXGMOdP0C3tbAgQNDm8Yy\nsHcXAA477LBU1rzk7P0GYn5xXYNC4yvYj66eSc6tD8S1JC6++OJUfuyxx2Dyw7FO//Vf/5XKv/vd\n78LrfvOb34Q6x2nxmi0AMHXq1FTWGCjVD2tRtabxC5MnT05lDW484ogjQp31oz5ZjSP72Mc+lsqa\nx57XfFCfLAe2AzF+ide1aGwfOKbs8ccfhykcPkfsC9cYm/nz54c6r5/BWgKAq6++OpU1vkXjX9gf\nzX2ytgHAueeem8q6voJ6qXv06JHKGvuoSSc4Po1960C8plRbGr/I95yjjjoqtOn9h+OHjj32WJjC\n4Xss9wUaO6saYd8+x+kBcQ0RfR9rCYhxajoe0LVsOLbnkksuCW0a3MzxObpmj8aYLVu2LJU1HufW\nW29NZV0vR8c23Lfqemza73JsmB4/kx8ev02cuGMtUD2vPOYCgOeffz6VNVa3e/fuoc7rL3EZyF0X\n7Morr0xlHncCuTHbPB7nNcyAXD1pnCtfH7pdjc/hMYvuv64NmI1nbqxt/PjxoT59+vRU5hhPjnVm\nPHNjjDHGGGOMqQr8cGOMMcYYY4ypCtrUlvbyyy+nMttTNFWh2hZ4avnNN98MbbwdIFoI2I4BAH/+\n859Dna0bms5R7T+LFy9O5V/96lehTa0Kmr6UU1d+6UtfCm081QxES56m8tWpcbai8XQ2kDvNyFPR\nmhLT5IfTOF911VWpzNOiQG6KUp6uZf0AcepW0+iq9ljjagdS6yLrP9/0NhCneXXKl6d5gZieUvfv\nueeeS2W+VoHcNO9sy1Drp9qBODU0T1eb5vn4xz+eymyf1P7z6KOPDnXWiKYd55Tfag/W/oftGmrj\nZb0AMQ2/bkdTV7MmOG01kHsdMdOmTWuyTfvvp59+OtTZqqefyampAeD0009P5REjRqTy7bff3uTn\nmwx8bjntsdqz1q9fH+qcplnPz7Zt21JZtaXXAtt4dVyh53njxo2prKl79d7L30XT82qaa9Yi2/G1\n/pe//CW0sYUXiH20prXW48lppdUSbfLD54T1pVZAPT/cr6n9Su+9HDrAKdKB3H6YUzTrOPVzn/tc\nqP/2t79tcju6Ltp3vvOdUOf7+AMPPBDaND3+z372s0b3D8i1u7H1WVP0a5gJ21U57KIpPHNjjDHG\nGGOMqQr8cGOMMcYYY4ypCvxwY4wxxhhjjKkK2jTm5r333ktljh/RtHlPPPFEqLMnUVMec5pFIPqu\nb7zxxtCmqZQ5RkJT6rGnFgBmzJiRyj179gxtmv5WPbjsA9bUoZwGFYieXPYgAzH9JBA9wprSmY81\nEOM/1LNs8sOebua4444L9bfffjvU2e+t6Uw5xkVTQXKMDxD9u4cffnho05TffF1p7JfGbLFG1KvO\naVEBYP/992/yM/laUY1+/etfD3XW6UEHHRTaNBU0p7LctGkTTOHcdtttqcznfcKECeF1U6ZMCXWO\nQ9DYAU4lrnEp2n9yn67XhaaNZv2ovjU+h9PWaj+s94Zf//rXqax9MqPa1/TT7EfXVL66bAHHD+kx\nMvnh2BS+R2nfqSmcOT5A4wG5D9Z4Ek1pz3E12t9oulvelqYS1zhD3pbG9h5//PGhzjFvGiPEffI1\n11wT2jR+kWMZdKkBjYvk+CK9jk1+eAzJfRWnhQZy75k8ptA+TlN187IMei71nsn60f5RxxX/+q//\n2mSb3id0nM1x8jqG/fznPx/q3K5LoWgM2rPPPpvKZ5xxRmjjmH0AGDlyZCo/+uijaI5CZm5uALAG\nAN8trgWwEsCshn8Tc99mTIdhzZpKw5o1lYY1ayoNa7ZGKOTh5kbknux6AD8FcEjDv4dKvF/GtAZr\n1lQa1qypNKxZU2lYszVCIQ830wG82cjfOzXyN2PKAWvWVBrWrKk0rFlTaVizNUJrYm6+DOBSADMB\nXA1gg77gYx/7WCq/9NJLqax52NUfvWjRolS+6KKLQtvdd98d6uwvV8+hrvvBXm/+DCCuQwLEfOa8\nhgQA3HHHHaGuMRqjR49OZfYVA8C//Mu/hDrnIv/+978f2q699tpQZ7+3+s31czjWZ/jw4ak8depU\n1DDNahYAtm7dmsrstb7nnnvC63T9AD4/Gpc1a9asVFZvKa+PAUSfqq6Xoznyx4wZk8oay6YxFO++\n+24qn3jiiaGN10YBgMsvvzyVNZaNtXbWWWeFNl1fZPPmzancnAee32sveKIgzXLsIcfR6Lpaqp+6\nurpU5nMFxHOg8YAax8fxUhqvoPFc3/ve91L54osvDm2qJ76mNCZBYx0efvjhVNZ1EDgmSden0rV/\nuF37do0fWrlyZSrrPaWGKUizCxYsSGWOQ9SYqGOPPTbUd9ppp1TWez5vU1G/P68hpm0c3woAv/nN\nb1KZY9GA3PXpOC6C771A7no1fB3puiT8XTR+UveP45RUs88//3yo83pWfF3UOAVplmNEeD0vjcXT\n8SSfL+0nNBaV43U0jlb7PNai9k163rmf07af//znoa5rgfHn6vWp8UbcD2vczD//8z+HOscX6z1F\nx+8cm8SxmvpdshSbLe06AEMAHAxgFYCfFLkdY9oLa9ZUGtasqTSsWVNpWLNVSLEzN5wC5PcA/tLY\ni3iWoEuXLjlZO0zbs2bNmpxfFWqUgjQLxFmWQYMG5fxKZtqWtWvXhiwwNUxRmu3WrVvODI1pW1at\nWpUzu1WjFKxZnpXu1asX9t133zbcLaMsWLAgxxlQoxSs2fnz56fygAEDQuY+0z6sXLkyZxa/MYp9\nuBmAzBMuAJyHmHlix4vIFvPBBx+ktI061aZp6DitIaegA3LtV2z/0e3qlPU//uM/pvIPf/jDvK/l\nlI2cmg/InUbU1H6cClWniHWqjdNG8nQekGsh4ZSYanuaM2dOqLM1hdOpNjWFVwMUpFkA2G+//VJ5\n48aNaSpaLQaaavySSy5JZU0B+uCDD6byL3/5y9B24YUXhjqfL53W5TS1QNTB0qVLQ5umSeX0jl26\ndAltn/zkJ0Od7Taa4vbkk09O5SeffDK0sZ0TiNY9tYysWLEi1LM/fgwePDjnu9QoBWuWbWnr1q1L\nU/xq6WEbABBtFmrN4cGm2mnUisD2Fk3le8ghh4T6V77ylVRWe60+IHBq33zaAmL/rxa7Cy64IJUn\nTZoU2jRt66BBgxrdJpB73WT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GkWncg/po2U+qqRRVT6wZTd+osQ/vvvtuKh911FGhTT3C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\n67Y0lFKzQHnq1n1tdWHNNk1ZarYtH25mAhiGzBT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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f71381bfb90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[04/05] cost: 2219.6125\n"
     ]
    },
    {
     "data": {
      "image/png": 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65nR9mrqa7SNAXKX5lltuCW06jc4rI6u9Taei2U6RT9q8CqNgzQLR6sC6Vc3w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\nx4+7ctgfMeX5zVFds3Mb8t8z7JN948YNU/fHxvjPD5EmP+fGn8t+fNw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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7114388c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training done. \n"
     ]
    }
   ],
   "source": [
    "sess = tf.Session()\n",
    "sess.run(init)\n",
    "# mean_img = np.mean(mnist.train.images, axis=0)\n",
    "mean_img = np.zeros((784))\n",
    "# Fit all training data\n",
    "batch_size = 128\n",
    "n_epochs   = 5\n",
    "print(\"Strart training..\")\n",
    "for epoch_i in range(n_epochs):\n",
    "    for batch_i in range(mnist.train.num_examples // batch_size):\n",
    "        batch_xs, _ = mnist.train.next_batch(batch_size)\n",
    "        trainbatch = np.array([img - mean_img for img in batch_xs])\n",
    "        trainbatch_noisy = trainbatch + 0.3*np.random.randn(\n",
    "            trainbatch.shape[0], 784)\n",
    "        sess.run(optm, feed_dict={x: trainbatch_noisy\n",
    "                                  , y: trainbatch, keepprob: 0.7})\n",
    "    print (\"[%02d/%02d] cost: %.4f\" % (epoch_i, n_epochs\n",
    "        , sess.run(cost, feed_dict={x: trainbatch_noisy\n",
    "                                    , y: trainbatch, keepprob: 1.})))\n",
    "    if (epoch_i % 1) == 0:\n",
    "        n_examples = 5\n",
    "        test_xs, _ = mnist.test.next_batch(n_examples)\n",
    "        test_xs_noisy = test_xs + 0.3*np.random.randn(\n",
    "            test_xs.shape[0], 784)\n",
    "        recon = sess.run(pred, feed_dict={x: test_xs_noisy, keepprob: 1.})\n",
    "        fig, axs = plt.subplots(2, n_examples, figsize=(15, 4))\n",
    "        for example_i in range(n_examples):\n",
    "            axs[0][example_i].matshow(np.reshape(\n",
    "                test_xs_noisy[example_i, :], (28, 28))\n",
    "                , cmap=plt.get_cmap('gray'))\n",
    "            axs[1][example_i].matshow(np.reshape(\n",
    "                np.reshape(recon[example_i, ...], (784,))\n",
    "                + mean_img, (28, 28)), cmap=plt.get_cmap('gray'))\n",
    "        plt.show()\n",
    "print(\"Training done. \")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PRINT SHAPE OF THE NETWORK"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shape of layer 1 is (1, 28, 28, 1)\n",
      "Shape of layer 2 is (1, 4, 4, 64)\n",
      "Shape of layer 3 is (1, 7, 7, 32)\n",
      "Shape of layer 4 is (1, 4, 4, 64)\n",
      "Shape of layer 5 is (1, 7, 7, 32)\n",
      "Shape of layer 6 is (1, 14, 14, 16)\n",
      "Shape of layer 7 is (1, 28, 28, 1)\n"
     ]
    }
   ],
   "source": [
    "test_xs, _ = mnist.test.next_batch(1)\n",
    "test_xs_norm = np.array([img - mean_img for img in test_xs])\n",
    "recon = sess.run(pred, feed_dict={x: test_xs_norm, keepprob: 1.})\n",
    "layers = sess.run(cae(x, weights, biases, keepprob)['layers']\n",
    "                  , feed_dict={x: test_xs_norm, keepprob: 1.})\n",
    "for i in range(len(layers)):\n",
    "    currl = layers[i]\n",
    "    print ((\"Shape of layer %d is %s\") % (i+1, currl.shape,))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# CLOSE SESSION"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Session closed.\n"
     ]
    }
   ],
   "source": [
    "sess.close()\n",
    "print (\"Session closed.\")"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
